My dog died a little more than a year ago, he was around 17 when he died and had a lot of health problems. He had been with my family since I was born. I didn't find him dead though, like you, I found him laying on the carpet, curled up as though he was asleep, grasping for breath. My family and I sat there with him and comforted him until he passed away ten minutes after. 
I've only had a guinea pig die on me, and that's kind of how I found him.
He was lying in his cage, and he wasn't moving, his eyes were crusty, and he was having a hard time breathing. My mother had to go out for about 30 minutes, and while he was in his cage, I thought that he might just have drank too fast or something, and so I went back to playing RTB. I got hungry, so I went out to get some food, and I checked up on him. I saw him blink one last time, then his eyes just stayed open, and he stopped breathing. He lived for about 8 years.
And, Adio, I'm sorry about your dog. He looks like he was a good dog, too.
